Appl Math Optim 38:283–301 (1998)
1998 Springer-Verlag New York Inc.
Stochastic Games with Average Payoff Criterion
M. K. Ghosh
and A. Bagchi
Department of Mathematics, Indian Institute of Science,
Bangalore 560012, India
Department of Applied Mathematics, University of Twente,
P.O. Box 217, 7500 AE Enschede, The Netherlands
Communicated by A. Bensoussan
Abstract. We study two-person stochastic games on a Polish state and compact
action spaces and with average payoff criterion under a certain ergodicity condition.
For the zero-sum game we establish the existence of a value and stationary optimal
strategies for both players. For the nonzero-sum case the existence of Nash equilib-
rium in stationary strategies is established under certain separability conditions.
Key Words. Stochastic game, Stationary strategy, Value, Nash equilibrium,
AMS Classiﬁcation. 90D15, 93E05, 90D25.
We study noncooperative stochastic games on uncountable state and action spaces, and
with ergodic or limiting average payoff. Although there is a vast literature on general
state Markovdecision processes (MDP) with average payoff criterion, the corresponding
results on stochastic games seem to be very limited. For ﬁnite or countable state space
there are several papers, e.g., , , , , , and . Uncountable state and
action spaces arise quite often in practical problems. When the planning horizon is
inﬁnite, two usual payoff criteria that are treated are discounted payoff and limiting
Part of this research was performed when the ﬁrst author was visiting the University of Twente, The